As a jazz player, I have to say it's not imprecise at all. It's more precise in fact. The root is important, and it is (often) played, just not by those voices.
To expand on this a bit, you very rarely see specific voicings written out in charts, at least outside of big band arrangements and such.
The player chooses what voicings to use, often on the fly. Voicings like 7-9-3-5 for a ii chord are only the most basic one-hand voicings that can give some minimal voice leading in common progressions.
Once a player learns a lot of different voicings, and more voicing concepts, they will add other notes like the 11, 13, and yes the root. Two-handed spread voicings on piano might often have a root on top, or pass through a root via voice leading in a progression.
The simpler voicings are there for beginners to teach the theory, enough practice to play a bit, and to emphasize getting the root out of the low register where it muddies things with the bass.
So the important piece of information is the key and chord quality. For an E7 as a V7 chord, it really matters that the root is E (and that you're in the key of, and maybe resolving to D) even if you don't, right at some particular moment, play the E.
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As a jazz player, I have to say it's not imprecise at all. It's more precise in fact. The root is important, and it is (often) played, just not by those voices.
To expand on this a bit, you very rarely see specific voicings written out in charts, at least outside of big band arrangements and such.
The player chooses what voicings to use, often on the fly. Voicings like 7-9-3-5 for a ii chord are only the most basic one-hand voicings that can give some minimal voice leading in common progressions.
Once a player learns a lot of different voicings, and more voicing concepts, they will add other notes like the 11, 13, and yes the root. Two-handed spread voicings on piano might often have a root on top, or pass through a root via voice leading in a progression.
The simpler voicings are there for beginners to teach the theory, enough practice to play a bit, and to emphasize getting the root out of the low register where it muddies things with the bass.
So the important piece of information is the key and chord quality. For an E7 as a V7 chord, it really matters that the root is E (and that you're in the key of, and maybe resolving to D) even if you don't, right at some particular moment, play the E.